In a clinical trail 21 out of 700 patients taking a prescrip

In a clinical trail, 21 out of 700 patients taking a prescription drug complained of flulike symptoms. Suppose that is known that 2.3% of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than 2.3% of this drug’s users experience flulike symptoms as a side effect at the a= 0.01 level of significance?

What are the null and alternative hypotheses?

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.023
Ha:   p   >   0.023

As we see, the hypothesized po = 0.023.          
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.03      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[p^(1 - p^)/n] =    0.006447591      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.08567682      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.277621999  
significance level =    0.01
  
          
Comparing p and the significance value, we   FAIL TO REJECT THE NULL HYPOTHESIS.      

Thus, we conclude that there is no significant evidence that more than 2.3% of this drug\'s users experience flulike symptoms.